“…Its popularity has increased rapidly in the reliability field and various versions, such as auxiliary PF [ 1 ], regularized PF [ 2 ] and unscented PF [ 3 ], are proposed to improve the performance of the standard particle filtering algorithm. The standard PF algorithm and its variants have been implemented for diagnostics and prognostics in a wide range of applications, including life prediction of batteries and fuel cells [ 4 , 5 , 6 , 7 ], degradation assessment and prediction in gears and bearings [ 8 , 9 , 10 ], health monitoring and prognostics of gas turbines [ 11 ], machine tools [ 12 ], and pumps [ 13 , 14 ], and also, in damage estimation and prediction of composite materials [ 15 , 16 , 17 , 18 ]. More application examples can be found in a recent review paper on the PF algorithm by Jouin et al [ 19 ].…”